I am not an expert on time series, and perhaps other colleagues will
help you with that part. But to respond to part of your post:
On 15 Jun 2003, helen-louise wrote:
> I am using the aggregate variance method to analyse a time
> series. This method has the following steps:
> a) Calculate the mean of the entire data set, <C>
> b) Divide the data set into N bins of width T
> c) Calculate the mean of each bin, <Ci> for i=1,2,..., N
> d) Sum over all bins {(<Ci> - <C>)^2}
> e) Take the square root, divide by N
Are you sure about this? I would have thought you'd divide by N (or
possibly by N-1), then take the square root; and as you conjectured
later (below), that would indeed be a standard deviation rather than a
variance.
> f) Repeat for next N
>
> You end up with a list of T values and corresponding "aggregated
> variance" values. Plot log T against the log of this variance gives
> a line with gradient m or gamma, which is always 0 or negative. This
> can be used as an estimator for other constants such as the Hurst
> exponent, eg. gamma is 2H - 2, and it is regarded as an indicator of
> self-similarity or fractality in the data.
Since log (variance) = log (standard deviation, squared)
= 2 log (standard deviation), the only problem here is that the
gradient will be off by a factor of 2 (except that I believe, as you
conjectured, that you have not correctly calculated the standard
deviation, which is too small by a factor of (square root of N), I
suspect).
> My problem is this: I have a data set with a lot of gaps or holes in
> the data.
< snip, 5 possible ways of dealing with missing data >
> Which of these techniques is correct?
Probably all of them are correct, or at least acceptable; at least in
some contexts and under some conditions. If there is a definitive
"correct" method for your situation, perhaps someone else can assist you
on this point. I would be inclined to ask, "What difference do any of
them make?" If you get answers that are so similar as to be
indistinguishable when you try applying all five methods, clearly the
choice of method is substantively and/or methodologically immaterial,
and you can pick the one that's easiest to carry out (or to justify, or
is otherwise convenient). If you get noticeably different results, that
would be interesting (and possibly worth a paper?), and the effort of
trying to figure out why those differences occur might be well repaid.
> If you can give a citation of a book or research paper to back up
> your answer, this would be wonderful.
>
> I am also now having a minor crisis about step (e) above, if I
> really am supposed to take the square root method from did so,
That sentence fragment doesn't make a whole lot of syntactic sense...
> but I can't seem to find this confirmed by any formulae online.
> However I admit to not being very good at maths.
> Am I calculating the standard deviation rather than the variance?
Not exactly (see above), but maybe [(std. dev.)/(sq.rt. of N)].
> And is my method wrong?
Yes, I think so: see comment above.
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Donald F. Burrill [EMAIL PROTECTED]
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